During his tenure, Bobins structured a $10 million loan for a potential buyer of troubled rival Exchange National Bank. In 1981, Exchange convinced Bobins to join the bank as senior executive vice president. By employing Bobins's strategies, Exchange grew from a $500 million bank in 1981 into a $3.2 billion Chicago giant by 1989.

In 1990, Netherlands-based giant ABN AMRO Bank purchased Exchange, merged it with ABN AMRO subsidiary LaSalle Bank in 1990, and named Bobins chairman of the merged bank in 1992. By 2003, he was chairman, president, and CEO of LaSalle Bank and president and CEO of LaSalle Bank Corporation (North American subsidiary of ABN AMRO Bank N.V.). Bobins led the bank through the largest uninterrupted period of growth in its 75-year history.